Precalculus Examples

$\log_{n} (\frac{4}{n})$

Step 1

Rewrite $\log_{n} (\frac{4}{n})$ as $\log_{n} (4) - \log_{n} (n)$ .

$\log_{n} (4) - \log_{n} (n)$

Step 2

Logarithm base $n$ of $n$ is $1$ .

$\log_{n} (4) - 1 \cdot 1$

Step 3

Multiply $- 1$ by $1$ .

$\log_{n} (4) - 1$

Step 4

Simplify each term.

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Step 4.1

Rewrite $\log_{n} (4)$ as $\log_{n} (2^{2})$ .

$\log_{n} (2^{2}) - 1$

Step 4.2

Expand $\log_{n} (2^{2})$ by moving $2$ outside the logarithm.

$2 \log_{n} (2) - 1$